Consider a two-dimensional surface in an Alexandrov space of curvature bounded above by k. Assume that this surface does not admit contracting deformations (a particular case of such surfaces is formed by area minimizing surfaces). Then this surface inherits the upper curvature bound, that is, this surface has also curvature bounded above by k, with respect to the intrinsic metric induced from its ambient space.
|Original language||English (US)|
|Number of pages||8|
|Journal||Electronic Research Announcements of the American Mathematical Society|
|State||Published - Apr 8 1999|
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